Related papers: Quantitative Constraints for Stable Sampling on th…
The recovery of multivariate functions and estimating their integrals from finitely many samples is one of the central tasks in modern approximation theory. Marcinkiewicz--Zygmund inequalities provide answers to both the recovery and the…
Let $\cM$ be a Brakke flow of $n$-dimensional surfaces in $R^N$. The singular set $\cS\subset\cM$ has a stratification $\cS^0\subset\cS^1\subset...\cS$, where $X\in \cS^j$ if no tangent flow at $X$ has more than $j$ symmetries. Here, we…
We prove a Marcinkiewicz-Zygmund type inequality for random variables taking values in a smooth Banach space. Next, we obtain some sharp concentration inequalities for the empirical measure of $\{T, T^2, \cdots, T^n\}$, on a class of smooth…
Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski-signature correlators, in contrast to the…
We establish quantitative estimates for sampling (dominating) sets in model spaces associated with meromorphic inner functions, i.e. those corresponding to de Branges spaces. Our results encompass the Logvinenko-Sereda-Panejah (LSP) Theorem…
We derive quantitative stability results for Minkowski bodies, as well as their counterparts, the $L_p$-Minkowski bodies in the range $1 \le p \neq n$. We prove that, for every pair of probability measures $\mu,\nu$ satisfying a…
We investigate projection constants for spaces of bihomogeneous harmonic and bihomogeneous polynomials on the unit sphere in finite-dimensional complex Hilbert spaces. Using averaging techniques, we demonstrate that the minimal norm…
We show several variants of concentration inequalities on the sphere stated as subgaussian estimates with optimal constants. For a Lipschitz function, we give one-sided and two-sided bounds for deviation from the median as well as from the…
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for…
We study the relationship between sampling sequences in infinite dimensional Hilbert spaces of analytic functions and Marcinkiewicz-Zygmund inequalities in subspaces of polynomials. We focus on the study of the Hardy space and the Bergman…
In this paper, we prove estimates and quantitative regularity results for the harmonic map flow. First, we consider H^1_loc-maps u defined on a parabolic ball P\subset M\times R and with target manifold N, that have bounded Dirichlet-energy…
We consider a randomly forced Ginzburg-Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the…
Let ${\mathbb X}$ be a compact, connected, Riemannian manifold (without boundary), $\rho$ be the geodesic distance on ${\mathbb X}$, $\mu$ be a probability measure on ${\mathbb X}$, and $\{\phi_k\}$ be an orthonormal system of continuous…
We prove that an approximated version of the Brunn--Minkowski inequality with volume distortion coefficient implies a Gaussian concentration-of-measure phenomenon. Our main theorem is applicable to discrete spaces.
Volume estimates of metric balls in manifolds find diverse applications in information and coding theory. In this paper, some new results for the volume of a metric ball in unitary group are derived via various tools from random matrix…
We prove that on an essentially non-branching $\mathrm{MCP}(K,N)$ space, if a geodesic ball has a volume lower bound and satisfies some additional geometric conditions, then in a smaller geodesic ball (in a quantified sense) we have an…
Existence of solution of the logarithmic Minkowski problem is proved for the case where the discrete measures on the unit sphere satisfy the subspace concentration condition with respect to some special proper subspaces. In order to…
Given a sphere with Bartnik data close to that of a round sphere in Euclidean 3-space, we compute its Bartnik-Bray outer mass to first order in the data's deviation from the standard sphere. The Hawking mass gives a well-known lower bound,…
We apply a new and mathematically rigorous method for the quantization of constrained systems to two-dimensional gauge theories. In this method, which quantizes Marsden-Weinstein symplectic reduction, the inner product on the physical state…
We study various generalizations of concentration of measure on the unit sphere, in particular by means of log-Sobolev inequalities. First, we show Sudakov-type concentration results and local semicircular laws for weighted random matrices.…